Options Backtesting With Realistic IV Surface

When to Use

Invoke this skill when backtesting options strategies (e.g. delta-neutral straddles, vertical spreads, calendar spreads, iron condors) and every leg is currently being priced at a single ATM volatility. A flat IV misprices in two directions at once: across strikes it ignores the equity put skew, so OTM put hedges are systematically bought too cheaply in the backtest; and across expirations it ignores the fact that skew is far steeper for a one-week option than a two-year one, so a calendar or diagonal appears to earn a spread that does not exist. This skill evaluates $\sigma(K/S, T)$ from a quadratic moneyness smile whose offset decays as a power law in $T$, then prices European options and Greeks on it with Black-Scholes-Merton.

When NOT to Use

• On American-style options where early exercise matters. The engine prices European exercise only. Every listed US single-stock option is American, and this engine will underprice ITM puts and calls on a stock about to go ex-dividend. Do not use it to decide whether to exercise — see early-exercise-assignment-risk-management and american-vs-european-style-option-exercise-handling.
• To calibrate a surface to live market quotes. get_strike_iv evaluates a closed form; it does not fit quotes and it does not check calendar or butterfly no-arbitrage constraints. For that, use options-implied-volatility-surface-construction.
• Across a discrete cash dividend without adjusting spot yourself. Only a continuous yield $q$ is modelled. Discrete dividends must be removed from $S$ by the caller before pricing.
• As a fill simulator. It returns theoretical mid prices with no spread, no slippage and no exercise/assignment mechanics. Pair it with execution-realistic-simulation and transaction-cost-analysis-tca-integration.

Prerequisites

• Underlying price series $S$ (already adjusted for discrete dividends paid before expiry), strike $K$, time to expiration $T$ in years, and risk-free rate $r$.
• ATM implied volatility $\sigma_{\text{atm}}$ for the tenor being priced.
• Smile parameters $\alpha$ (skew slope) and $\beta$ (smile curvature), calibrated at the 30-day reference tenor — quoting $\alpha$ without its tenor is meaningless.
• Term-decay exponent $\gamma$ (skew_term_decay, default $0.5$) and continuous dividend yield $q$ (default $0$).

Workflow

1. Evaluate the surface $\sigma(m, T)$:

   • Moneyness $m = K/S$; smile offset $\text{offset} = \alpha (m - 1) + \beta (m - 1)^2$.
   • Term scale $s(T) = \min\left(4.0,; (T_{\text{ref}}/T)^{\gamma}\right)$ with $T_{\text{ref}} = 30/365$, so $s(T_{\text{ref}}) = 1$. $$\sigma(m, T) = \sigma_{\text{atm}} + \left[\alpha (m - 1) + \beta (m - 1)^2\right] \cdot s(T)$$
   • Decision point — $\alpha$ and $\beta$ are tenor-anchored. They describe the smile at $T_{\text{ref}}$, not at every expiration. Re-fitting them per expiration and leaving $s(T)$ on double-counts the term decay; set skew_term_decay=0.0 if you calibrate per tenor.
   • Decision point — a clamped IV is not a quote. If the engine logs a clamp at MIN_STRIKE_IV/MAX_STRIKE_IV, the quadratic has been extrapolated past its valid range. Narrow the strike universe rather than trading the clamped value.

2. Price with Black-Scholes-Merton at the strike IV:

   • $d_1 = \dfrac{\ln(S/K) + (r - q + \tfrac{1}{2}\sigma^2) T}{\sigma \sqrt{T}}$, $\quad d_2 = d_1 - \sigma\sqrt{T}$.
   • $\text{Call} = S e^{-qT} N(d_1) - K e^{-rT} N(d_2)$, $\quad \text{Put} = K e^{-rT} N(-d_2) - S e^{-qT} N(-d_1)$.
   • Decision point — both legs of a spread at the same strike must use the same $\sigma$. The surface depends on moneyness, not on call/put, so put-call parity holds exactly. If it does not, something downstream is rounding or re-deriving IV per leg.

3. Settle expiring positions on intrinsic value, not on an epsilon tenor.

   • tte_years=0 returns the terminal payoff with zero time value, zero gamma and is_expired=True. A negative tenor raises — it means the backtest clock ran past expiry without settling the contract.

4. Aggregate Greeks and rebalance the delta hedge on net portfolio delta $\sum \Delta_i$, remembering theta is per calendar day and vega is per one volatility point.

5. Audit the skew drag: re-run the backtest with skew_alpha=0.0, smile_beta=0.0 and difference the P&L. That gap is the mispricing a flat-IV backtest was booking as alpha.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

• Pricing OTM puts at flat ATM volatility. At $\sigma_{\text{atm}} = 20%$, $\alpha = -0.30$, $\beta = 0.50$, a 30-day $K/S = 0.90$ put's IV is $23.5%$, not $20%$. A backtest that buys crash protection at the ATM vol books a hedge cost it could never have paid, and the error compounds every roll.
• Applying one smile at every expiration. Skew is not flat in $T$: with $\gamma = 0.5$ the same $10%$-OTM put carries roughly $2\times$ the skew offset at one week that it carries at one month, and about $0.2\times$ at two years. A calendar spread backtested on a $T$-invariant smile earns a spread that does not exist in the market.
• Flooring theoretical prices at a minimum tick. Returning $$0.01$ for an option worth $10^{-9}$ invents premium on exactly the wings a short-premium backtest is supposed to let expire worthless, and it breaks put-call parity. Quantize to the tick at the fill-simulation layer, never inside the pricer.
• Rounding the theoretical price to cents. Rounding a $$100$ ATM straddle's legs to $$0.01$ shifts $C - P$ off $S e^{-qT} - K e^{-rT}$ by a fraction of a cent per leg — which is larger than the edge most spread strategies are trying to measure.
• Accepting an unrecognised option type. Any pricer that treats "not a call" as "a put" will silently return a put price for "C". Assert on the returned option_type rather than trusting the string you passed.
• Letting NaN reach the pricer. A NaN spot from a bad tick propagates through $d_1$ and can emerge as a plausible-looking price rather than an error. Reject non-finite market data at the boundary.
• Ignoring dividends in $d_1/d_2$. Continuous $q$ shifts the drift to $r - q$; discrete cash dividends before expiry require replacing $S$ with $S - \sum D_i e^{-r t_i}$ before pricing. Neither is optional for single-name equity backtests.
• Assuming options are never assigned early. European pricing on an American contract omits the early-exercise premium entirely.

Verification

• With OptionsIVSurfaceEngine(risk_free_rate=0.10, skew_alpha=0.0, smile_beta=0.0), price $S=42$, $K=40$, $T=0.5$, $\sigma=0.20$: the call is $$4.76$ and the put $$0.81$, reproducing the standard Black-Scholes worked example in Hull.
• Confirm $\sigma(0.90, 30\text{d}) = 0.235$ exactly for $\alpha=-0.30$, $\beta=0.50$, $\sigma_{\text{atm}}=0.20$ — the documented formula applied undamped at the reference tenor.
• Confirm put-call parity: $C - P = S e^{-qT} - K e^{-rT}$ to at least 10 decimal places, on the skewed surface and with $q > 0$.
• Confirm each analytic Greek matches a central finite difference of the price function.
• Confirm $s(4 T_{\text{ref}}) = 0.5$ and $s(T_{\text{ref}}/4) = 2.0$ — the $T^{-1/2}$ decay.
• Run python -m unittest discover -s skills/options-backtesting-with-realistic-iv-surface/scripts and confirm 100% pass rate.

Related Skills

• options-implied-volatility-surface-construction
• vectorized-vs-event-driven-backtest-tradeoffs
• transaction-cost-analysis-tca-integration
• options-greeks-real-time-portfolio-aggregation
• early-exercise-assignment-risk-management
• american-vs-european-style-option-exercise-handling
• execution-realistic-simulation